Functions introducing eastern European school of painting’s style (7)

I believe the answer is:

sienese

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'school of painting's style' is the definition.
'Sienese' can be an answer for 'school' (I have seen 'School of painting' mean 'sienese' so perhaps 'school' could also mean 'sienese'). I'm not sure about the 'of painting's style' bit.

'functions introducing eastern european' is the wordplay.
'functions' becomes 'sines' (sine is a kind of function).
'introducing' indicates putting letters inside (some letters introduced or inserted into others).
'eastern' becomes 'e'.
'european' becomes 'e' (abbreviation e.g. EU).
'sines' enclosing 'e' is 'sienes'.
'sienes'+'e'='SIENESE'

Can you help me to learn more?

(Other definitions for sienese that I've seen before include "From Sienna" , "A native of Siena" , "Of an Italian city famed for a school of painting" .)

I've seen this clue in The Times.

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